Q-universal desingularization

Edward Bierstone*, Pierre D. Milman, Michael Temkin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We prove that the algorithm for desingularization of algebraic varieties in characteristic zero of the first two authors is functorial with respect to regular morphisms. For this purpose, we show that, in characteristic zero, a regular morphism with connected affine source can be factored into a smooth morphism, a ground-field extension and a generic-fibre embedding. Every variety of characteristic zero admits a regular morphism to a Q-variety. The desingularization algorithm is therefore Q-universal or absolute in the sense that it is induced from its restriction to varieties over Q. As a consequence, for example, the algorithm extends functorially to localizations and Henselizations of varieties.

Original languageAmerican English
Pages (from-to)229-250
Number of pages22
JournalAsian Journal of Mathematics
Issue number2
StatePublished - Jun 2011


  • Canonical
  • Functorial
  • Marked ideal
  • Resolution of singularities


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